Stochastic Geometry Perspective of Massive MIMO Systems

Owing to its ability to improve both spectral and energy efficiency of wireless networks, massive multiple-input multiple-output (mMIMO) has become one of the key enablers of the fifth-generation (5G) and beyond communication systems. For successful integration of this promising physical layer technique in the upcoming cellular standards, it is essential to have a comprehensive understanding of its network-level performance. Over the last decade, stochastic geometry has been instrumental in obtaining useful system design insights of wireless networks through accurate and tractable theoretical analysis. Hence, it is only natural to consider modeling and analyzing the mMIMO systems using appropriate statistical constructs from the stochastic geometry literature and gain insights for its future implementation.

With this broader objective in mind, we first focus on modeling a cellular mMIMO network that uses fractional pilot reuse to mitigate the sole performance-limiting factor of mMIMO networks, namely, pilot contamination. Leveraging constructs from the stochastic geometry literature, such as Johnson-Mehl cells, we derive analytical expressions for the uplink (UL) signal-to-interference-and-noise ratio (SINR) coverage probability and average spectral efficiency for a random user. From our system analysis, we present a partitioning rule for the number of pilot sequences to be reserved for the cell-center and cell-edge users that improves the average cell-edge user spectral efficiency while achieving similar cell-center user spectral efficiency with respect to unity pilot reuse. In addition, using the analytical approach developed for the cell-center user performance evaluation, we study the performance of a small cell system where user and base station (BS) locations are coupled. The impact of distance-dependent UL power control on the performance of an mMIMO network with unity pilot reuse is analyzed and subsequent system design guidelines are also presented.

Next, we focus on the performance analysis of the cell-free mMIMO network, which is a distributed implementation of the mMIMO system that leads to the second and third contributions of this dissertation. Similar to the cellular counterpart, the cell-free systems also suffer from pilot contamination due to the reuse of pilot sequences throughout the network. Inspired by a hardcore point process known as the random sequential adsorption (RSA) process, we develop a new distributed pilot assignment algorithm that mitigates the effect of pilot contamination by ensuring a minimum distance among the co-pilot users. This pilot assignment scheme leads to the construction of a new point process, namely the multilayer RSA process. We study the statistical properties of this point process both in one and two-dimensional spaces by deriving approximate but accurate expressions for the density and pair correlation functions. Leveraging these new results, for a cell-free network with the proposed RSA-based pilot assignment scheme, we present an analytical approach that determines the minimum number of pilots required to schedule a user with probabilistic guarantees. In addition, to benchmark the performance of the RSA-based scheme, we propose two optimization-based centralized pilot allocation schemes using linear programming principles. Through extensive numerical simulations, we validate the efficacy of the distributed and scalable RSA-based pilot assignment scheme compared to the proposed centralized algorithms.

Apart from pilot contamination, another impediment to the performance of a cell-free mMIMO is limited fronthaul capacity between the baseband unit and the access points (APs). In our fourth contribution, using appropriate stochastic geometry-based tools, we model and analyze the downlink of such a network for two different implementation scenarios. In the first scenario, we consider a finite network where each AP serves all the users in the network. In the second scenario, we consider an infinite network where each user is served by a few nearby APs in order to limit the load on fronthaul links. From our analyses, we observe that for the finite network, the achievable average system sum-rate is a strictly quasi-concave function of the number of users in the network, which serves as a key guideline for scheduler design for such systems. Further, for the user-centric architecture, we observe that there exists an optimal number of serving APs that maximizes the average user rate.

The fifth and final contribution of this dissertation focuses on the potential improvement that is possible by the use of mMIMO in citizen broadband radio service (CBRS) spectrum sharing systems. As a first concrete step, we present comprehensive modeling and analysis of this system with omni-directional transmissions. Our model takes into account the key guidelines by the Federal Communications Commission for co-existence between licensed and unlicensed networks in the 3.5 GHz CBRS frequency band. Leveraging the properties of the Poisson hole process and Matern hardcore point process of type II, a.k.a. ghost RSA process, we analytically characterize the impact of different system parameters on various performance metrics such as medium access probability, coverage probability, and area spectral efficiency. Further, we provide useful system design guidelines for successful co-existence between these networks. Building upon this omni-directional model, we also characterize the performance benefits of using mMIMO in such a spectrum sharing network.